Bulinskii, Alexandre; Doukhan, Paul Inégalités de mélange fort utilisant des normes d’Orlicz. (Strong mixing moment inequalities using Orlicz norms). (French) Zbl 0659.60009 C. R. Acad. Sci., Paris, Sér. I 305, 827-830 (1987). We first extend the Orlicz inequality for covariances given by the first author [On strong mixing conditions for random fields and central limit theorem, Sov. Math., Dokl. (to appear)] to the Hilbert valued case. After this we show generalizations of the Marcinkiewicz-Zygmund inequality of higher order moments for sums of strongly mixing random variables extending to Orlicz case results by the second author and F. Portal [ibid. 297, Sér. I, 129-132 (1983; Zbl 0544.62022)] and the second author, J. Léon and F. Portal [ibid. 298, Sér. I, 305-308 (1984; Zbl 0557.60006)]. Orlicz norms allow weakening of moment assumptions. Interest of the results is explicited by the example of kernel density estimates. Cited in 1 Document MSC: 60B05 Probability measures on topological spaces 60E15 Inequalities; stochastic orderings Keywords:Orlicz inequality; Marcinkiewicz-Zygmund inequality; Orlicz norms Citations:Zbl 0544.62022; Zbl 0557.60006 PDFBibTeX XMLCite \textit{A. Bulinskii} and \textit{P. Doukhan}, C. R. Acad. Sci., Paris, Sér. I 305, 827--830 (1987; Zbl 0659.60009)